Chapter 15.

Boost Power Factor Correction

Maximum Peak to Peak Ripple Current in the Boost PFC Inductor:

Because the switching frequency is usually more than
three orders of magnitude higher than the line frequency, for a single
switching cycle the inductor can be considered as having a triangle AC
switching current with the instantaneous line current as a DC bias. After
making this approximation, the following equations can be developed:

In general, for an inductor the following equation will apply:

(15-1)

When the switch is ON, the current in the boost inductor will increase from
Il
to
Ih:

(15-2)

Where Vi
is the instantaneous input voltage.

When the switch is OFF, the current in the boost inductor will decrease from
Ih
to Il:

(15-3)

We will eliminate now D between equations (15-2) and (15-3):

(15-4)

To find at what instantaneous input voltage the peak to
peak ripple current will have a maximum, we need to analyze the function:

(15-5)

From the above equation, we see that:

a) If the instantaneous input voltage can reach half of
the boost voltage, the peak to peak ripple current has a maximum in this point.
This maximum is:

(15-6)

The maximum instantaneous RMS value will be:

(15-7)

b) If the instantaneous input voltage cannot reach half
of the boost voltage, the peak to peak ripple current has a maximum when the
instantaneous input line reach its peak.

In a normal design, 85-276Vac, or 176-276Vac, or
85-138Vac, the instantaneous input voltage would always reach a value equal
with half of the boost voltage. The only situation when the instantaneous input
voltage will not reach half of the boost voltage, is in a 85-136Vac design with
400Vdc boost voltage witch is unusual. This particular case will not be
discussed further.

RMS Ripple Current in the Boost PFC Inductor:

Re-write the formula (15-4) function of time:

The RMS value of this current will be:

Boost PFC Inductor Calculation:

We will try now to determine a formula for calculating
the boost inductor having as input data: PFC output power, PFC boost voltage,
Minimum AC input voltage, PFC switching frequency and Maximum boost ripple
current as a percentage from the peak Input AC current:

(15-8)

Maximum Boost PFC Inductor Peak Current:

Analyzing the above equation, the conclusion will be
that the inductor peak current will occur at the minimum AC line voltage (V
rms
),
and when the instantaneous line voltage reaches its peak. Therefore, the
maximum peak current in the boost inductor will be:

Now, going back to the equations (15-2) and (15-3) and eliminating ripple current,
we will have the following equation for the Boost duty cycle: